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Subject: New Game: DITION rss

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Lisandro Iaffar
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DITION

Characteristics

The essential idea behind the development of this game was to create a mechanism that would allow literally infinite possibilities of development, always keeping the maximum simplicity of the game, while keeping to the minimum the dimensions of the board. Ie not wanted to achieve a very large number of possibilities via increasing dimensions of the board, but actually achieve infinite number possibilities with finite dimensions. I am aware that the property of "infinite possibilities" does not necessarily imply a high degree of complexity. Analyzing the subject I found that a way to achieve endless possibilities in a space of finite dimensions is eliminating the mechanics of boxes and introducing another type of metrics.
I was essentially inspired by the game of chinese origin here known as "GO" which is characterized by extremely simple rules and at the same time maintaining a high degree of complexity. The dynamics of this game is quite similar to the GO, share many aspects, and in fact the purpose is similar, and yet at the same time, they also differ substantially in many aspects. This will be understood by analyzing the rules of the game.
The rules were analyzed consistently with certain typical aspects of war.

The name of the game derives from the Latin expression for the word "dominion / control".

Equipment

Pieces:
The pieces are circular and its diameter is d, with a thickness that allows its easy handling. These are characterized by that each of them defines a circular domain around itself whose perimeter is at a distance D from the perimeter of the piece, where D=3xd. Each piece has one side painted white and the other black (like in Othello), and each player may chose one side (color) to play. Both sides have in the center a gray circle (its just decorative), whose diameter is equal to d/4. For a piece of a specific color, the domain of another piece of the same color will be an allied domain, and vice versa.
As in the GO, it is assumed that virtually there is an infinite supply of pieces.

Board:
The board has two concentric squares: the peripheral (whose side is equal to 20xd) and the central (whose side is equal to 20xd-2xD=14xd). The peripheral defines the playing area, and the central only serves as a visual aid to comply with the rule of "appearance". The peripheral also defines a domain, which is precisely the domain that is delimiting the central square. This domain is neutral.




Rods of Measurement:
These rods only serve to facilitate the verification of the distances between pieces (That is, to say if a piece is contained in the domain of another piece -then the "vice versa" is implied-). Their use is not mandatory, they are just a tool to avoid uncertainty.
The rods (one for each player -o the same for the two in a rigorous case), will be of a length equal to D-d=2xd . Thus, the measurement is accomplished by placing the rod over the two respective pieces, and may mean that the pieces are at a distance of 2xd or less (in practice it will always be less) between them if the rod is supported by both pieces (given this case, then a piece contains the other in its domain and vice versa). This will always ensure a secure measurement. Because of this, it is more practical for the rod to be as follows:






Rules

- Start: At the start of the game the board is empty. Black plays first. Then both players play alternately. In his turn, a player must make appear a piece in an empty space on the board, abiding to the rules listed below.

- Appearance: A piece appears contained in an no-opponent domain.

- Disappearance : A piece disappears contained in an opponent triad.

- End: When one of the players makes a "suicide" move, the game ends, and that player loses.



Notes about used terms:
Note 1: see the descriptions of the pieces and the board to understand the definition of "domain".
Note 2: the area resulting from the intersection of at least three allied domains is called "triad".
Note 3: it is said that a player makes a "suicide" move when he makes appear a piece in a place where it is contained in an opponent triad, and since this move does not make opponent pieces disappear (then, only that allied piece disappears, by the rule of disappearance).
Note 4: it is said that a player makes a "sacrifice" move when he makes appear a piece in a place where it is contained in an opponent triad, and since this move makes one or more opponent pieces disappear (then, that allied piece and the respective opponent pieces disappears, by the rule of disappearance).





------------------------------------------------------------------------

Considerations on the Rules

All considerations below are not written as "additional rules"; but arise entirely from the analysis of the Rules of the Game. None of the rules have exceptions to any situation. Heeding the rules, you will find that any apparent ambiguity is removed. Here, I take the trouble to explain and help to ensure the correct interpretation of them and avoid disputes:

The rule is clear, the piece must be contained in an no-opponent domain to appear; it is irrelevant if in that the area where you want to make appear a piece is also covered by one or two opponent domains. If they become three, the same criteria applies, except that in this case, if such action does not eliminate any opponent pieces, it will be a "suicide", and the player who makes that move lose the game.

What is said in the first paragraph also applies to notes listed after the statement of the rules of the game.

 
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Rey Alicea
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Really love the minimalist appearance.
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Lisandro Iaffar
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Thank you very much! Coming from you means a lot, because I've seen some posts and comments of yours, and i saw you have a lot of experience. I really would appreciate any comments you could make about the game, especially those that point out any mistakes I may have made.
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Rey Alicea
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Libertador wrote:
Thank you very much! Coming from you means a lot, because I've seen some posts and comments of yours, and i saw you have a lot of experience. I really would appreciate any comments you could make about the game, especially those that point out any mistakes I may have made.


Kind words Lisandro, but I have to say that I'm the least experienced here. Russ Williams, Nick Bentley, Christian Freeling, Luis Bolanos Mures are more experienced.
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Lisandro Iaffar
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hahah i will still apreciate any observation you could make. Tanks for that names! I will try to talk whit them!
 
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This looks cool! And thanks for the illustrations. Are there any plans for a digital implementation? I only ask because while I suspect it plays just fine over-the-board, the digital format could allow for overlays indicating domains for improved clarity. Of course I am a bit biased given that I do most of my board gaming digitally.

At first glance I suspected the continuous space to be only a gimmick, especially when I read about the measuring rods. But after the rest of the description I came to feel that all the elements of the design hang together quite nicely. So yeah, not quite the expert feedback you were looking for but I hope some more folks take a look at your game!
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Russ Williams
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To be honest, I found the rules a bit long and confusing to follow and I did not take a lot of time to read them carefully now due to other things going on (sorry!), so my comments will be brief and meta...

Continuous space is a strange thing in a game for me, as it leads to physically ambiguous positions ("Are these 2 pieces touching or not?", "Are these 2 pieces 1.99 centimeters apart or 2.01 centimeters apart?", "Oh shit, I just touched this piece and I'm not sure if it moved or not, what should we do?", "Oops, I slightly bumped the table; the game is ruined and cannot be reconstructed...", etc.) None of these problems come up in a normal game with discrete locations. In practice, I've found that continuous space games lead to a need for both players to "be sporting" and resolve such ambiguities somehow (flip a coin, submit to the will of the player who seems more sure, submit to the will of the player who's taking their turn, submit to the will of the more pushy forceful aggressive personality, etc), which for me is highly undesirable and seems a significant drawback in a game intended for serious competitive play. (As opposed to a light short abstract game like Coin Clusters, or many historical miniatures wargames played more for the visual spectacle and the simulation value and the story/experience.)

For what it's worth, I know of another vaguely similar sounding continuous space abstract strategy game Calculus.
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Richard Moxham
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russ wrote:
To be honest, I found the rules a bit long and confusing to follow and I did not take a lot of time to read them carefully now due to other things going on (sorry!), so my comments will be brief and meta...

Continuous space is a strange thing in a game for me, as it leads to physically ambiguous positions ("Are these 2 pieces touching or not?", "Are these 2 pieces 1.99 centimeters apart or 2.01 centimeters apart?", "Oh shit, I just touched this piece and I'm not sure if it moved or not, what should we do?", "Oops, I slightly bumped the table; the game is ruined and cannot be reconstructed...", etc.) None of these problems come up in a normal game with discrete locations. In practice, I've found that continuous space games lead to a need for both players to "be sporting" and resolve such ambiguities somehow (flip a coin, submit to the will of the player who seems more sure, submit to the will of the player who's taking their turn, submit to the will of the more pushy forceful aggressive personality, etc), which for me is highly undesirable and seems a significant drawback in a game intended for serious competitive play. (As opposed to a light short abstract game like Coin Clusters, or many historical miniatures wargames played more for the visual spectacle and the simulation value and the story/experience.)

For what it's worth, I know of another vaguely similar sounding continuous space abstract strategy game Calculus.

Hi.

FWIW, this was exactly my own reaction - except that Russ has a limitless stock of useful parallels, whereas I once played Monopoly (unless I'm misremembering and it was actually someone else).

But the basic idea sounds interesting, so I hope you're able to overcome what sounds like a potential stumbling-block. Maybe FauxSloMo's suggestion of a digital implementation would do the trick.

Your rules definitely need revising for greater clarity, though. Don't cut corners on that - it really matters.
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Lisandro Iaffar
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FauxSloMo wrote:
This looks cool! And thanks for the illustrations. Are there any plans for a digital implementation? I only ask because while I suspect it plays just fine over-the-board, the digital format could allow for overlays indicating domains for improved clarity. Of course I am a bit biased given that I do most of my board gaming digitally.

At first glance I suspected the continuous space to be only a gimmick, especially when I read about the measuring rods. But after the rest of the description I came to feel that all the elements of the design hang together quite nicely. So yeah, not quite the expert feedback you were looking for but I hope some more folks take a look at your game!


THANK YOU FauxSloMo!!!

I am glad you like it!!!, and about a digital version: of course I always had that in mind but I wanted to specifically design the game so that you could play without problems in the physical board. But a digital version has interested me from the beginning mostly by the fact that you mentioned: in a digital version you could constantly visualize domains, which would make it easier to visualize the situation on the board, and avoid the need for the rods.

If you want to make a digital version of this game, or know someone who might be interested in doing so; go ahead! I do not work as a game designer nor am I interested in getting some economic benefit of this game. I designed this game because I needed to. See, initially I do like very much to play chess ... but over time this game lost its charm for me, because I realized it was a deterministic game, because your chances of development were finite, and that is why a computer can play and win even to the best chess player in the world. Then I started playing GO, and I'm passionate of its simplicity and complexity, but again, it was a deterministic game ... with a HUGE number of possibilities, but not infinite ......So I arose a real need (a thirst, rather) to invent a game like this.

I would appreciate you to invite your friends to review this game! ALL feedback is welcome! Thanks You Again!
 
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Lisandro Iaffar
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russ wrote:
To be honest, I found the rules a bit long and confusing to follow and I did not take a lot of time to read them carefully now due to other things going on (sorry!), so my comments will be brief and meta...

Continuous space is a strange thing in a game for me, as it leads to physically ambiguous positions ("Are these 2 pieces touching or not?", "Are these 2 pieces 1.99 centimeters apart or 2.01 centimeters apart?", "Oh shit, I just touched this piece and I'm not sure if it moved or not, what should we do?", "Oops, I slightly bumped the table; the game is ruined and cannot be reconstructed...", etc.) None of these problems come up in a normal game with discrete locations. In practice, I've found that continuous space games lead to a need for both players to "be sporting" and resolve such ambiguities somehow (flip a coin, submit to the will of the player who seems more sure, submit to the will of the player who's taking their turn, submit to the will of the more pushy forceful aggressive personality, etc), which for me is highly undesirable and seems a significant drawback in a game intended for serious competitive play. (As opposed to a light short abstract game like Coin Clusters, or many historical miniatures wargames played more for the visual spectacle and the simulation value and the story/experience.)

For what it's worth, I know of another vaguely similar sounding continuous space abstract strategy game Calculus.


Russ, thank you very much for your observations!

Absolutely everything you said; literally, I have taken into account when designing this game, and yes, in many aspects, I decided that what I got made it worth the risk.

First of all: I live in Argentina, I speak Spanish, so I will probably may have misspoken in some paragraphs, which may have led to you confused. That is entirely my responsibility, of course, and I apologize if that is the case.

"I found the rules a bit long": The rules are no longer than the GO. In fact, this game has 5 rules while GO has 6.

"and confusing to follow": This really worries me!!! It would be very helpful if you clear this point as far as you can!!!

"Are these 2 pieces touching or not?" : if Two pieces are touching each other or not is irrelevant to the game. I understand that you may have mentioned it only as an example, but I clarify in case.

"Are these 2 pieces 1.99 centimeters or 2.01 centimeters apart apart?" Rods completely avoid this uncertainty.

"Oh shit, I just touched this piece and I'm not sure if it moved or not, what should we do?": That's a risk! Players are expected to prevent that from happening

"Oops, I slightly bumped the table, the game is ruined and can not be reconstructed ...": this is also a risk! but I do not think it's bigger than the risk to a normal game of go. Using biconvex chips may well cancel that risk (as with the GO). For stronger shocks, the game would be so ruined as one of GO.

Of course, what you mention IS a weak point of the game, I had even thought of proposing the only use pieces with magnets, (which is actually a laudable option), but I decided to take the risk.

Many games require "sportsmanship" from his players; like airsoft ... but the result is worth it. I know exactly what you mean, I repeat that I thought much about it, but again, in the end I decided to take the risk.

"For what it's worth, I know of another similarly sounding vaguely abstract continuous space strategy game" Thanks for the tip! I just watched the game from the link you gave me. It basically has the same problems, and from what I saw, they released a digital version. That is also something that interests me a lot for this game! Of course, when I thought of a board without divisions, immediately look for examples on the Internet. I had only found a game called "Constellations".
 
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Lisandro Iaffar
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mocko wrote:
russ wrote:
To be honest, I found the rules a bit long and confusing to follow and I did not take a lot of time to read them carefully now due to other things going on (sorry!), so my comments will be brief and meta...

Continuous space is a strange thing in a game for me, as it leads to physically ambiguous positions ("Are these 2 pieces touching or not?", "Are these 2 pieces 1.99 centimeters apart or 2.01 centimeters apart?", "Oh shit, I just touched this piece and I'm not sure if it moved or not, what should we do?", "Oops, I slightly bumped the table; the game is ruined and cannot be reconstructed...", etc.) None of these problems come up in a normal game with discrete locations. In practice, I've found that continuous space games lead to a need for both players to "be sporting" and resolve such ambiguities somehow (flip a coin, submit to the will of the player who seems more sure, submit to the will of the player who's taking their turn, submit to the will of the more pushy forceful aggressive personality, etc), which for me is highly undesirable and seems a significant drawback in a game intended for serious competitive play. (As opposed to a light short abstract game like Coin Clusters, or many historical miniatures wargames played more for the visual spectacle and the simulation value and the story/experience.)

For what it's worth, I know of another vaguely similar sounding continuous space abstract strategy game Calculus.

Hi.

FWIW, this was exactly my own reaction - except that Russ has a limitless stock of useful parallels, whereas I once played Monopoly (unless I'm misremembering and it was actually someone else).

But the basic idea sounds interesting, so I hope you're able to overcome what sounds like a potential stumbling-block. Maybe FauxSloMo's suggestion of a digital implementation would do the trick.

Your rules definitely need revising for greater clarity, though. Don't cut corners on that - it really matters.


Thanks for your observations Richard!!
Please, describe me what you think its not clear about the rules! Thanks for your time!
 
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Clifford Jones
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Here's an idea for a physical version that requires less measurement. Print the pieces on transparency sheets of diameter d+D. Have the central region of the piece be opaque and the outer region be translucent. Then you won't need the measuring rod.
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While I generally side with Russ in my opinion of continuous space games as played in meatspace, I'd like to see iOS implementations of games like this. Apps could eliminate all ambiguity, and along with it the need to be sporting.

Speaking of which, there is an iOS implementation of a "continuous space" connection game called Clara.

But I also agree: the rules of DITION are a bit confusing.
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Lisandro Iaffar
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penncajones wrote:
Here's an idea for a physical version that requires less measurement. Print the pieces on transparency sheets of diameter d+D. Have the central region of the piece be opaque and the outer region be translucent. Then you won't need the measuring rod.


Thank you for the Tip Clifford! I had thought of that in a particular instance of the development; but it turned out not to be a practical idea. Anyway, if you have any other ideas, feel free to say it!
 
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milomilo122 wrote:
While I generally side with Russ in my opinion of continuous space games as played in meatspace, I'd like to see iOS implementations of games like this. Apps could eliminate all ambiguity, and along with it the need to be sporting.

Speaking of which, there is an iOS implementation of a "continuous space" connection game called Clara.

But I also agree: the rules of DITION are a bit confusing.


It took me an hour and a half to read your comment because my vision was constantly diverted to that gif you have hahahah.

I would like you, if you have time, to show me an example of some ambiguity that comes to you. Or is it that is not understood what the rules refer? You consider that the correct thing would be to explain with pictures, or must rewrite the rules, or should I do both?

That game, Clara, has an identical element to my game, on the issue of distance. And not only that: during the development of my game, a game derived from the development was one exactly like this! just, I considered it of lower interest regarding my main goal. Thank you for show it to me!

Thanks for your Time!!
 
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Russ Williams
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(Warning, mathematical/computational pedantry ahead!)
milomilo122 wrote:
While I generally side with Russ in my opinion of continuous space games as played in meatspace, I'd like to see iOS implementations of games like this. Apps could eliminate all ambiguity, and along with it the need to be sporting.

I don't believe that apps could eliminate all ambiguity. Computers cannot represent arbitrary real numbers, after all, and the usual methods of perform computing arithmetic on real numbers (with finite precision) have some degree of error due to truncation and rounding, which creeps in, and the error accumulates as more and more operations are performed.

Granted, there exist arbitrary precision arithmetic libraries which could be used in principle (e.g. storing the fraction "1/3" as a closed form fraction made of the exact integers "1" and "3" instead of as the binary analogue of "0.33333" which is truncated), but then the operations become slower and slower as the expressions get larger and larger.

And still, the vast majority of real numbers are not representable in such closed forms, or indeed in ANY finite form! This unavoidable mathematical fact seems fundamentally significant to me in the context of "pure strategy" games using a continuum.

The intended purpose of continuous space in an abstract strategy game like this is to make it more strategic and give the player infinitely many options from the continuum. I.e. the difference between placing a piece at location (3.4567,2.22234) and (3.45671,2.222338) can sometimes matter significantly, and supposedly the player can make that distinction.

But then appears the question of user interface: how does the user actually specify exactly where a piece is going? Simply clicking on a screen is quite insufficient and imprecise; there are after all only finitely many pixels on a screen. (Even a rather small finite number if played on a tiny screen like a smart phone.) Clicking on a screen position to select an exact real coordinate is analogous to playing Go but instead of specifying the exact intersection for the piece you play, there is a bit of random fuzz added to your intended move, so that you might want to play e.g. on the 4,4 point but your stone ends up on the 3,4 point. Of course in the case of a "continuous space" game, the error would be smaller, but the inherent imprecision is fundamentally there, and fundamentally nullifying the design goal of providing infinite choice to the player.

Letting a user type real numbers ("3.45646778644, 11.3423342342") would be rather cumbersome, and even that would not really give access to all possible real numbers, but only to a relatively tiny subset of the real numbers. The vast majority of real numbers are not finitely representable in any way.

And similarly, how would the program report information back to the player about the positions of pieces? Simply seeing shapes on a screen is not at all precise, and reporting coordinates back in a form like "4.3414895" is in general not giving the true position either - rounding and approximation necessarily occurs. Reporting in an exact form (as represented by an arbitrary precision library) would typically give very complex expressions with fractions, powers, roots, etc barely useful for a human reader.

And the details of an implementation (how it represents real numbers, how its user interface works, etc) would literally determine what moves are legal, which seems strange. Different programs for a discrete game like Go or Chess would not diverge in game state or decisions about whether a move is legal merely due to different inaccuracies in how they treat "real" numbers. For me, philosophically the very rules of the game should not be defined by a particular software implementation; rather, it should be the inverse: a software implementation should faithfully capture the rules of the game, so that 2 different apps always agree.

Thus fundamentally it seems to me that there isn't really going to be infinite freedom of choice for the player in continuous space in any case. The goal of truly allowing a player access to the entire continuum is not merely impractical, but literally mathematically impossible.
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Richard Moxham
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russ wrote:
(Warning, mathematical/computational pedantry ahead!)
milomilo122 wrote:
While I generally side with Russ in my opinion of continuous space games as played in meatspace, I'd like to see iOS implementations of games like this. Apps could eliminate all ambiguity, and along with it the need to be sporting.

I don't believe that apps could eliminate all ambiguity.

[...a lot of closely-argued detail...]

Thus fundamentally it seems to me that there isn't really going to be infinite freedom of choice for the player in continuous space in any case. The goal of truly allowing a player access to the entire continuum is not merely impractical, but literally mathematically impossible.


Just like to say that, in addition to reading very impressively (even to a guzinta) as an analysis of the problem, this post represented an incredibly generous donation of personal time.

Respect, Russ.
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Russ Williams
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mocko wrote:
Just like to say that, in addition to reading very impressively (even to a guzinta) as an analysis of the problem, this post represented an incredibly generous donation of personal time.

Respect, Russ.

Thanks... This site has too many interesting addictive threads...! (Especially when I am trying to reduce my computer time due to a sore arm...)
 
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I should've spoken more precisely. I agree that, for the reasons you describe, digital implementation wouldn't eliminate all ambiguity.

Rather, it would just eliminate the ambiguity that most annoys me about continuous games.

The vagaries of discretization and the imprecision of placing a piece aren't really annoying to me (speaking as a player) compared the annoyance of having to decide whether, e.g. a piece is or is not "contained in the domain", as in the game above. If the software adjudicates that stuff, my main discomfort with these games is erased.

Another way to say this is that I care more about having a definitive answer over which there can be no arguing, rather than an answer that conforms to what is right for some ideal, truly continuous version of such a game.
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Libertador wrote:

It took me an hour and a half to read your comment because my vision was constantly diverted to that gif you have hahahah.


Heh. I only just created this avatar yesterday. Maybe that was a bad idea.

Quote:
I would like you, if you have time, to show me an example of some ambiguity that comes to you. Or is it that is not understood what the rules refer? You consider that the correct thing would be to explain with pictures, or must rewrite the rules, or should I do both?


It's the way the rules are written. On reading it a second time I now understand it. I think it's a little wordy and could be improved with different orgnization.

If I were writing the rules, one thing I'd do is give the term "domain" its own definition so it can be found by quick scanning, since it's such a central part of the game.

I'll try to come back here a rewrite a little chunk to illustrate my meaning, but I've got to get to real work here.

Quote:
That game, Clara, has an identical element to my game, on the issue of distance. And not only that: during the development of my game, a game derived from the development was one exactly like this! just, I considered it of lower interest regarding my main goal. Thank you for show it to me!


I didn't mean to imply Clara is a good game, just that it's an example of an iOS implementation of a continuous space game.
 
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Lisandro Iaffar
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Russ, I really Really appreciate your time!! My respect sr. In your last comment, regarding an implementation of the game on the computer, you are right in every word. But again, literally, I had already taken into account every one of the things you've said so far (...until now...). That is, I had even taken into account what you said about the pixels, and of course also about the inaccuracies of the computer. Why? because I'm an engineering student, and like any other student I must handle those basic issues relating to computers (with respect to programming, I've only used Pithon). So knowing this, what I find so interesting about a digital implementation of this game? : All that "FauxSloMo" and "What`s New "have said.

That is, in a digital aplication this game could be played only approximately, but also more practically . Regarding the user interface , I had thought of that , and it's not that complicated : if you've ever used a CAD program , you will see that there they have already dealt with the problem that occurs when a user must make moves very precisely only with mause . A very important tool used in these programs , and that I intended to use in a digital implementation , is what is known as " inference " , a tool that performs many calculations for the user presents the results graphically (indicating directions of movement, optimal positions, using colors to indicate levels, etc), not in numbers , allowing you to make precise and convenient movements. The other element is the "zoom " , which allows you to make your movements as precise as you want. The issue of to arrange them, so they are easily accessible, is resolved in these CAD programs (the function of "inference" does not require access, this action is automatic, making it a very handy tool). I had thought that this game could be played in a tablet easily.

Talking about the physical board, the rods completely eliminate uncertainty about the distances between parts (the rod is supported by two pieces, or falls, no intermediate points). One thing to note is that the use of the rods does not allow us to harness all the infinity that allows the game theoretically, but the subset of possibilities in that allows us to move, is also infinite.

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What`s New wrote:
"I'll try to come back here a rewrite a little chunk to illustrate my meaning, but I've got to get to real work here."

Thank you!! I'll be waiting!
 
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Lisandro Iaffar
Argentina
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3 Items:
- I do not have the means to market this game, but also want it to become known: anyone know if offer it to someone else to sell it on his own is a convenient idea?
- I was forgetting to ask! What you think about the name of the game? you like?
- (I have noticed that in a rigurous game, the players should use the same measuring rod,...and that small diferences and imperfections regarding the diameter of the pieces can not be "canceled", so they must be reduced to a practical minimum...just like in football the arches do not have the same dimensions, but the diferences are insignificant)
 
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Lisandro Iaffar
Argentina
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Im working now on a digital version of the game.
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Lisandro Iaffar
Argentina
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I think the mechanics of this game could be applied to the development of themed games, with some variations, such as the variation of domain size of a piece, in certain circumstances ...You can think of a game where there are different types of pieces; with different functions ... strong pieces that only die when they are contained in 4 (or more) domains of weak pieces and in turn these weak pieces die when they are contained in 2 (or less) domains of other stronger pieces ... pieces that are something like "dropships" that only serve to provide a domain where pieces can be born ... etc
 
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